The “There was an error returning the category list from Discourse” error message in your screenshot indicates that there is a problem with the plugin’s configuration. If you go to the WP Discourse Connection settings tab, are you seeing a notice saying that “You are connected to Discourse”?
For the API Key field on that page, have you entered an All Users API Key? If not, could you try changing the API Key to an All Users API Key? On Discourse the key should be generated like this:
For the WP Discourse Publishing Username field, try using the name of the Discourse system user. Unless you have edited that username on Discourse, you should enter system into the Publishing Username field.